A) \[{{\tan }^{-1}}4\]
B) \[{{\cot }^{-1}}4\]
C) \[{{\tan }^{-1}}2\]
D) \[{{\cot }^{-1}}2\]
Correct Answer: B
Solution :
\[y=2{{e}^{2x}}\] ...(i) |
\[\therefore \,\,\,\,\frac{dy}{dx}=2.\,\,{{e}^{2x}}.2=4.\,\,{{e}^{2x}}\] |
\[\therefore \,\,\,\,\left( \frac{dy}{dx} \right)at\,\,P=4\] |
\[\therefore \,\,\,\,\tan \theta =4\] \[\Rightarrow \theta ={{\tan }^{-1}}4\] |
\[\therefore \] required angle \[=90-\theta =\frac{\pi }{2}-{{\tan }^{-1}}4\] |
\[={{\cot }^{-1}}4\] |
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